Charge transport through one-dimensional Moiré crystals

Abstract

Moiré superlattices were generated in two-dimensional (2D) van der Waals heterostructures and have revealed intriguing electronic structures. The appearance of mini-Dirac cones within the conduction and valence bands of graphene is one of the most striking among the new quantum features. A Moiré superstructure emerges when at least two periodic sub-structures superimpose. 2D Moiré patterns have been particularly investigated in stacked hexagonal 2D atomic lattices like twisted graphene layers and graphene deposited on hexagonal boron-nitride. In this letter, we report both experimentally and theoretically evidence of superlattices physics in transport properties of one-dimensional (1D) Moiré crystals. Rolling-up few layers of graphene to form a multiwall carbon nanotube adds boundaries conditions that can be translated into interference fringes-like Moiré patterns along the circumference of the cylinder. Such a 1D Moiré crystal exhibits a complex 1D multiple bands structure with clear and robust interband quantum transitions due to the presence of mini-Dirac points and pseudo-gaps. Our devices consist in a very large diameter (>80 nm) multiwall carbon nanotubes of high quality, electrically connected by metallic electrodes acting as charge reservoirs. Conductance measurements reveal the presence of van Hove singularities assigned to 1D Moiré superlattice effect and illustrated by electronic structure calculations.

Giant spin signals in chemically functionalized multiwall carbon nanotubes

“…1 where τ e and τ sf are the free adjustable parameters, constant in energy, corresponding to the charge and spin lifetime; l e and l sf are the associated mean free paths; D and v are the charge carrier diffusion coefficient and velocity, respectively; DOS is the nanotube density of states per unit of length; and σ and ρ are the nanotube conductivity and resistivity, respectively. The energy-dependent density of states and charge carrier velocity of a pristine zigzag triple-wall CNT (TWCNT) of ~80 nm diameter, more precisely a (1045,0)@(1054,0)@(1063,0) TWCNT, were previously computed using tight-binding calculations in ( 60 ). All these quantities, as obtained with parameters τ e = 80 × 10 −12 s and τ sf = 10 4 × τ e = 800 × 10 −9 s, can be found in fig.…”

Moiré patterns in van der Waals heterostructures

“…To understand the MPs, we use two methods: a simple superposition model (SSM) and an analytical model [75]. While approaches similar to our SSM have previously been applied in an ad-hoc way to several all-hexagonal systems [23,33,35,[77][78][79][80], here we demonstrate a consistent methodology that can in principle be applied to any system including those with mixed symmetry. MPs observed on α-Bi grown on HOPG have been successfully modeled previously using a commensurate model [44].…”

Observation of Drastic Electronic-Structure Change in a One-Dimensional Moiré Superlattice

“…While there has been a rapid progress on understanding the moiré physics in 2D heterostructures, experimental studies on moiré superlattice in one-dimensional (1D) systems are still limited, and no clear evidence on strong electronic structure modification has been made and explained in structure-identified 1D moiré superlattices [17][18][19][20]. Double-wall carbon nanotubes (DWCNTs), which correspond to a "rolled up" version of twisted bilayer graphene, naturally provide an ideal platform to experimentally probe the moiré physics in 1D.…”